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QUESTION 4 25 P A 4 noded quadrilateral element is shown below 4 1 2 X The (x, y) coordinates (in mm) of each node
QUESTION 4 25 P A 4 noded quadrilateral element is shown below 4 1 2 X The (x, y) coordinates (in mm) of each node of the 4-noded quadrilateral element shown in the figure above are given in the tables below: node X 2 6 y 6 5The (x, y) coordinates (in mm) of each node of the 4-noded quadrilateral element shown in the figure above are given in the tables below: node 2 3 X 2 5 6 N y 1 6 5 1) Determine the Jacobian matrix [J] and [J]-1 for the element. (20 marks) 2) Evaluate the integral below using 2 x 2 Gauss-Legendre quadrature: (5 marks) 1 = (x + y) dxdy where A denotes the region shown in figure above. Note: Change of variables formula (from x, y coordinates to , n coordinates) for double integrals is given by f(x,y) dxdy = f(x (5, n), y (5, n)) UldEdn where IJI is the determinant of the Jacobian matrix [J]
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